A291316 Expansion of x/(1-x) + x^4*(1-x)/(1-x^3) + x^7*(1-x)*(1-x^3)/(1-x^5) + ... in powers of x.

1, 1, 1, 2, 0, 1, 3, -1, 1, 2, 0, 2, 1, 0, -1, 4, 2, -1, 2, -3, 4, 3, -1, 2, 0, 1, 1, 2, -2, 2, 5, 2, -3, 0, 1, -1, 6, 0, 4, -2, -1, 3, -1, 2, 0, 4, -2, 2, 4, -2, 1, 5, -2, -2, -2, 3, 6, 1, 3, -2, 4, -3, -1, -2, 3, 6, 2, 0, -4, 5, 1, 3, -1, 0, 0, 4, -1, -2, 4

Offset: 1

Author

Michael Somos, Aug 22 2017

Keywords

• sign

Examples

			G.f. = x + x^2 + x^3 + 2*x^4 + x^6 + 3*x^7 - x^8 + x^9 + 2*x^10 + ...
		

Links

• George E. Andrews, The Bhargava-Adiga Summation and Partitions, 2016. See equation (1.5)

Crossrefs

Cf. A008443, A143064, A290735, A290737.

Programs

PARI

{a(n) = my(A); if( n<0, 0, A = x * O(x^n); A = sum(k=0, (n-1)\3, x^(3*k+1) * prod(i=1,k, 1 - x^(2*i-1), 1 + A) / (1 - x^(2*k+1)) ); polcoeff(A, n))};

Formula

a(n) = A008443(n) - A290735(n) = A290737(n) - A143064(n).